0132_0231_1023_1230
Counting sequence:
1, 1, 2, 6, 20, 66, 217, 717, 2393, 8086, 27677, 95914, 336192, 1190476, 4253706, 15319805, 55559535, 202731750, 743762565, 2741791950, 10150796340, 37726100580, 140701234590, 526415398770, 1975209064194, 7430977818876, 28024302694802, 105924899086132, 401202252605168, 1522531417039192, 5788273568603316, 22042448722590877, 84072084066351675, 321131247165805958, 1228325770029872661, 4704458927940267622, 18040094616421444364, 69258251129454446836, 266183275226386551446, 1024098261009881748390, 3943947388241658062846, 15202952463057715449492, 58655990874652000923814, 226498904000208417440268, 875330529796690278173856, 3385434364165727492554152, 13103226106582294950240204, 50751597139229466703775538, 196705200909360003925859766, 762894420044634607038289884, 2960629478908621682759316162, 11496455072333229731647682124, 44667739174745151890152357032, 173645921201743951427092367976, 675408903305144623666009583340, 2628403538245382020926747115716, 10233691516271036234160118973892, 39863919243444097403568190886712, 155355931302626828065396999796868, 605715940515863464330389465684456, 2362636897643495133712663046128032, 9219462328986603571192135841621424, 35990589447306401331878005938932712, 140553440745743035583293165498933341, 549108072849945895207172907917817171, 2146015811231949172982115208819679430, 8389998783314519432297720844298258485, 32812561834149426933481069554090774870, 128369904072151702460916737263581842940, 502373705070998782017437711612672056980, 1966650291030107341504675254346458083910, 7701229474287077686212162884834051231070, 30166293911127233700377600350472619146790, 118197764689202163108544497587849636607780, 463253348399784163953998108868164072641950, 1816128582529134418736291649657226501021980, 7121806951626116559131000548069006063392960, 27934850821387710461007439875311883724984200, 109600406873067615994664909604175589365262940, 430115242379504369072595127174799752294557990, 1688346838804270226047327924045688648799087650, 6628878906037992204166574116738195695190880500, 26032602696529175861150763607856423076013948310, 102256701932274433323522805855461170201949254500, 401754123721175469485336781667916126498084928600, 1578777914309612880080332617572224489662205747000, 6205427758120696463994436353237211331887074197700, 24395532826310899872514679375777232782292316195580, 95925657700797013482483814618894284425175473852700, 377262133046275384383909736702313127015788033156680, 1483999393754239327376196138201563585164122193842620, 5838543159706365643870349961143788634277133442497240, 22974907750016615212927219872523729343707618960779680, 90423199612081401988259277111562222483008574611210960, 355943555973315388708553913693008169570554216123189720, 1401380206583490090693669594253700869740044431865218290, 5518268943060165943347141295850879153460395073966788830, 21733030692325875932978374120356067685917957573966408860, 85606516300146106003274965131643019347306461063554769570, 337257062120514249500617899509552789656924366406515281180, 1328867311180801070589569450850860325016931616799335669240
Generating function in Maple syntax:
((-x^3-x+1)*(1-4*x)^(1/2)+3*x^3+2*x^2+x-1)/(4*x^2-2*x)
Generating function in latex syntax:
\frac{\left(-x^{3}-x +1\right) \sqrt{1-4 x}+3 x^{3}+2 x^{2}+x -1}{4 x^{2}-2 x}
Generating function in sympy syntax:
(3*x**3 + 2*x**2 + x + sqrt(1 - 4*x)*(-x**3 - x + 1) - 1)/(4*x**2 - 2*x)
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*F(x)^2-(2*x-1)*(3*x^3+2*x^2+x-1)*F(x)+x^6+2*x^5+5*x^4+x^2-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(3 x^{3}+2 x^{2}+x -1\right) F \! \left(x \right)+x^{6}+2 x^{5}+5 x^{4}+x^{2}-3 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 66
a(6) = 217
a(n+5) = 4*(-3+2*n)/(n+6)*a(n)-6*(n-1)/(n+6)*a(1+n)+(20+9*n)/(n+6)*a(n+2)-2*(27+7*n)/(n+6)*a(n+3)+(34+7*n)/(n+6)*a(n+4), n >= 7
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 66
a \! \left(6\right) = 217
a \! \left(n +5\right) = \frac{4 \left(-3+2 n \right) a \! \left(n \right)}{n +6}-\frac{6 \left(n -1\right) a \! \left(1+n \right)}{n +6}+\frac{\left(20+9 n \right) a \! \left(n +2\right)}{n +6}-\frac{2 \left(27+7 n \right) a \! \left(n +3\right)}{n +6}+\frac{\left(34+7 n \right) a \! \left(n +4\right)}{n +6}, \quad n \geq 7
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21219/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[148,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[6,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[11,x]*F[14,x,k[0]]
F[14,x,k[0]] = F[139,x,k[0]]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x]+F[66,x,k[0]]
F[16,x] = F[17,x]+F[35,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[11,x]*F[20,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[1,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[21,x]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[27,x]
F[27,x] = F[1,x]+F[25,x]
F[28,x] = F[29,x]+F[30,x]+F[34,x]
F[29,x] = 0
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[11,x]+F[32,x]
F[32,x] = F[29,x]+F[30,x]+F[33,x]
F[33,x] = F[11,x]*F[25,x]
F[34,x] = F[11,x]*F[24,x]
F[35,x] = F[36,x]+F[42,x]
F[36,x] = F[37,x]
F[37,x] = F[11,x]*F[38,x]
F[38,x] = F[27,x]+F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[11,x]*F[39,x]
F[42,x] = F[29,x]+F[43,x]+F[53,x]
F[43,x] = F[11,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[25,x]
F[46,x] = F[47,x]
F[47,x] = F[29,x]+F[43,x]+F[48,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = F[25,x]+F[50,x]
F[50,x] = F[29,x]+F[48,x]+F[51,x]
F[51,x] = F[11,x]*F[52,x]
F[52,x] = F[25,x]+F[50,x]
F[53,x] = F[11,x]*F[54,x]
F[54,x] = F[24,x]+F[55,x]
F[55,x] = F[50,x]+F[56,x]
F[56,x] = F[29,x]+F[57,x]+F[62,x]+F[65,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[33,x]
F[60,x] = 2*F[29,x]+F[57,x]+F[61,x]
F[61,x] = F[11,x]*F[50,x]
F[62,x] = F[11,x]*F[63,x]
F[63,x] = F[32,x]+F[64,x]
F[64,x] = F[29,x]+F[57,x]+F[61,x]+F[62,x]
F[65,x] = F[11,x]*F[55,x]
F[66,x,k[0]] = F[67,x,k[0]]+F[96,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[71,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]*F[8,x,k[0]]
F[70,x,k[0]] = F[1,x]+F[68,x,k[0]]
F[71,x,k[0]] = F[29,x]+F[72,x,k[0]]+F[77,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]*F[8,x,k[0]]
F[73,x,k[0]] = F[25,x]+F[74,x,k[0]]
F[74,x,k[0]] = F[29,x]+F[72,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[11,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[68,x,k[0]]+F[74,x,k[0]]
F[77,x,k[0]] = F[11,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[86,x,k[0]]
F[79,x,k[0]] = F[68,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[29,x]+F[81,x,k[0]]+F[85,x,k[0]]
F[81,x,k[0]] = F[8,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[11,x]+F[83,x,k[0]]
F[83,x,k[0]] = F[29,x]+F[81,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[11,x]*F[68,x,k[0]]
F[85,x,k[0]] = F[11,x]*F[79,x,k[0]]
F[86,x,k[0]] = F[74,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[29,x]+F[88,x,k[0]]+F[92,x,k[0]]+F[95,x,k[0]]
F[88,x,k[0]] = F[8,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = F[59,x]+F[90,x,k[0]]
F[90,x,k[0]] = 2*F[29,x]+F[88,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[11,x]*F[74,x,k[0]]
F[92,x,k[0]] = F[11,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[83,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[29,x]+F[88,x,k[0]]+F[91,x,k[0]]+F[92,x,k[0]]
F[95,x,k[0]] = F[11,x]*F[86,x,k[0]]
F[96,x,k[0]] = F[108,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[103,x,k[0]]+F[29,x]+F[98,x,k[0]]
F[98,x,k[0]] = F[8,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[25,x]
F[100,x,k[0]] = F[101,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[11,x]
F[102,x,k[0]] = F[100,x,k[0]]+F[68,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[11,x]
F[104,x,k[0]] = F[102,x,k[0]]+F[105,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[97,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[105,x,k[0]]*F[11,x]
F[108,x,k[0]] = F[109,x,k[0]]+F[110,x,k[0]]+F[120,x,k[0]]+F[29,x]
F[109,x,k[0]] = 0
F[110,x,k[0]] = F[11,x]*F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[74,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[109,x,k[0]]+F[110,x,k[0]]+F[115,x,k[0]]+F[29,x]
F[115,x,k[0]] = F[11,x]*F[116,x,k[0]]
F[116,x,k[0]] = F[100,x,k[0]]+F[117,x,k[0]]
F[117,x,k[0]] = 2*F[29,x]+F[115,x,k[0]]+F[118,x,k[0]]
F[118,x,k[0]] = F[11,x]*F[119,x,k[0]]
F[119,x,k[0]] = F[117,x,k[0]]+F[74,x,k[0]]
F[120,x,k[0]] = F[11,x]*F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[129,x,k[0]]
F[122,x,k[0]] = F[100,x,k[0]]+F[123,x,k[0]]
F[123,x,k[0]] = 2*F[29,x]+F[124,x,k[0]]+F[128,x,k[0]]
F[124,x,k[0]] = F[11,x]*F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]+F[83,x,k[0]]
F[126,x,k[0]] = 2*F[29,x]+F[124,x,k[0]]+F[127,x,k[0]]
F[127,x,k[0]] = F[100,x,k[0]]*F[11,x]
F[128,x,k[0]] = F[11,x]*F[122,x,k[0]]
F[129,x,k[0]] = F[117,x,k[0]]+F[130,x,k[0]]
F[130,x,k[0]] = 2*F[29,x]+F[131,x,k[0]]+F[135,x,k[0]]+F[138,x,k[0]]
F[131,x,k[0]] = F[11,x]*F[132,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[90,x,k[0]]
F[133,x,k[0]] = 3*F[29,x]+F[131,x,k[0]]+F[134,x,k[0]]
F[134,x,k[0]] = F[11,x]*F[117,x,k[0]]
F[135,x,k[0]] = F[11,x]*F[136,x,k[0]]
F[136,x,k[0]] = F[126,x,k[0]]+F[137,x,k[0]]
F[137,x,k[0]] = 2*F[29,x]+F[131,x,k[0]]+F[134,x,k[0]]+F[135,x,k[0]]
F[138,x,k[0]] = F[11,x]*F[129,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[11,x]*F[141,x,k[0]]*F[144,x]
F[141,x,k[0]] = F[142,x]+F[143,x,k[0]]
F[142,x] = F[1,x]+F[36,x]
F[143,x,k[0]] = F[68,x,k[0]]+F[97,x,k[0]]
F[144,x] = F[145,x]+F[22,x]
F[145,x] = F[1,x]+F[146,x]
F[146,x] = F[147,x]
F[147,x] = F[11,x]*F[144,x]
F[148,x] = F[149,x]
F[149,x] = F[11,x]*F[150,x]
F[150,x] = F[151,x]+F[16,x]
F[151,x] = F[152,x]
F[152,x] = F[11,x]*F[142,x]*F[144,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{148}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{35}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{42}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{29}\! \left(x \right)+F_{43}\! \left(x \right)+F_{53}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{25}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{29}\! \left(x \right)+F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{25}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{29}\! \left(x \right)+F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{25}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{24}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{50}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{29}\! \left(x \right)+F_{57}\! \left(x \right)+F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{33}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{11}\! \left(x \right) F_{50}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{32}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{29}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{55}\! \left(x \right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{68}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{72}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{72}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{81}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{81}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{88}\! \left(x , y\right)+F_{92}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{59}\! \left(x \right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{88}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{88}\! \left(x , y\right)+F_{91}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{29}\! \left(x \right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{25}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{110}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{109}\! \left(x , y\right) = 0
F_{110}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{110}\! \left(x , y\right)+F_{115}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{115}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{124}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{124}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{122}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{135}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = 3 F_{29}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{117}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{134}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{129}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{141}\! \left(x , y\right) F_{144}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x \right)+F_{143}\! \left(x , y\right)
F_{142}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{22}\! \left(x \right)
F_{145}\! \left(x \right) = F_{1}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{11}\! \left(x \right) F_{144}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{11}\! \left(x \right) F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{16}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{11}\! \left(x \right) F_{142}\! \left(x \right) F_{144}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_148(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_12(x, k_0) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_6(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_11(x)*F_14(x, k_0))
Eq(F_14(x, k_0), F_139(x, k_0) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x) + F_66(x, k_0))
Eq(F_16(x), F_17(x) + F_35(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_11(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_1(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_21(x))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_27(x))
Eq(F_27(x), F_1(x) + F_25(x))
Eq(F_28(x), F_29(x) + F_30(x) + F_34(x))
Eq(F_29(x), 0)
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_11(x) + F_32(x))
Eq(F_32(x), F_29(x) + F_30(x) + F_33(x))
Eq(F_33(x), F_11(x)*F_25(x))
Eq(F_34(x), F_11(x)*F_24(x))
Eq(F_35(x), F_36(x) + F_42(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_11(x)*F_38(x))
Eq(F_38(x), F_27(x) + F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_11(x)*F_39(x))
Eq(F_42(x), F_29(x) + F_43(x) + F_53(x))
Eq(F_43(x), F_11(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_25(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_29(x) + F_43(x) + F_48(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_25(x) + F_50(x))
Eq(F_50(x), F_29(x) + F_48(x) + F_51(x))
Eq(F_51(x), F_11(x)*F_52(x))
Eq(F_52(x), F_25(x) + F_50(x))
Eq(F_53(x), F_11(x)*F_54(x))
Eq(F_54(x), F_24(x) + F_55(x))
Eq(F_55(x), F_50(x) + F_56(x))
Eq(F_56(x), F_29(x) + F_57(x) + F_62(x) + F_65(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_33(x))
Eq(F_60(x), 2*F_29(x) + F_57(x) + F_61(x))
Eq(F_61(x), F_11(x)*F_50(x))
Eq(F_62(x), F_11(x)*F_63(x))
Eq(F_63(x), F_32(x) + F_64(x))
Eq(F_64(x), F_29(x) + F_57(x) + F_61(x) + F_62(x))
Eq(F_65(x), F_11(x)*F_55(x))
Eq(F_66(x, k_0), F_67(x, k_0) + F_96(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_71(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0)*F_8(x, k_0))
Eq(F_70(x, k_0), F_1(x) + F_68(x, k_0))
Eq(F_71(x, k_0), F_29(x) + F_72(x, k_0) + F_77(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0)*F_8(x, k_0))
Eq(F_73(x, k_0), F_25(x) + F_74(x, k_0))
Eq(F_74(x, k_0), F_29(x) + F_72(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_11(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_68(x, k_0) + F_74(x, k_0))
Eq(F_77(x, k_0), F_11(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_86(x, k_0))
Eq(F_79(x, k_0), F_68(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_29(x) + F_81(x, k_0) + F_85(x, k_0))
Eq(F_81(x, k_0), F_8(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_11(x) + F_83(x, k_0))
Eq(F_83(x, k_0), F_29(x) + F_81(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_11(x)*F_68(x, k_0))
Eq(F_85(x, k_0), F_11(x)*F_79(x, k_0))
Eq(F_86(x, k_0), F_74(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_29(x) + F_88(x, k_0) + F_92(x, k_0) + F_95(x, k_0))
Eq(F_88(x, k_0), F_8(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), F_59(x) + F_90(x, k_0))
Eq(F_90(x, k_0), 2*F_29(x) + F_88(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_11(x)*F_74(x, k_0))
Eq(F_92(x, k_0), F_11(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_83(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_29(x) + F_88(x, k_0) + F_91(x, k_0) + F_92(x, k_0))
Eq(F_95(x, k_0), F_11(x)*F_86(x, k_0))
Eq(F_96(x, k_0), F_108(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_103(x, k_0) + F_29(x) + F_98(x, k_0))
Eq(F_98(x, k_0), F_8(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_25(x))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_11(x))
Eq(F_102(x, k_0), F_100(x, k_0) + F_68(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_11(x))
Eq(F_104(x, k_0), F_102(x, k_0) + F_105(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_97(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_105(x, k_0)*F_11(x))
Eq(F_108(x, k_0), F_109(x, k_0) + F_110(x, k_0) + F_120(x, k_0) + F_29(x))
Eq(F_109(x, k_0), 0)
Eq(F_110(x, k_0), F_11(x)*F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_74(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_109(x, k_0) + F_110(x, k_0) + F_115(x, k_0) + F_29(x))
Eq(F_115(x, k_0), F_11(x)*F_116(x, k_0))
Eq(F_116(x, k_0), F_100(x, k_0) + F_117(x, k_0))
Eq(F_117(x, k_0), F_115(x, k_0) + F_118(x, k_0) + 2*F_29(x))
Eq(F_118(x, k_0), F_11(x)*F_119(x, k_0))
Eq(F_119(x, k_0), F_117(x, k_0) + F_74(x, k_0))
Eq(F_120(x, k_0), F_11(x)*F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_129(x, k_0))
Eq(F_122(x, k_0), F_100(x, k_0) + F_123(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_128(x, k_0) + 2*F_29(x))
Eq(F_124(x, k_0), F_11(x)*F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_83(x, k_0))
Eq(F_126(x, k_0), F_124(x, k_0) + F_127(x, k_0) + 2*F_29(x))
Eq(F_127(x, k_0), F_100(x, k_0)*F_11(x))
Eq(F_128(x, k_0), F_11(x)*F_122(x, k_0))
Eq(F_129(x, k_0), F_117(x, k_0) + F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0) + F_135(x, k_0) + F_138(x, k_0) + 2*F_29(x))
Eq(F_131(x, k_0), F_11(x)*F_132(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_90(x, k_0))
Eq(F_133(x, k_0), F_131(x, k_0) + F_134(x, k_0) + 3*F_29(x))
Eq(F_134(x, k_0), F_11(x)*F_117(x, k_0))
Eq(F_135(x, k_0), F_11(x)*F_136(x, k_0))
Eq(F_136(x, k_0), F_126(x, k_0) + F_137(x, k_0))
Eq(F_137(x, k_0), F_131(x, k_0) + F_134(x, k_0) + F_135(x, k_0) + 2*F_29(x))
Eq(F_138(x, k_0), F_11(x)*F_129(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_11(x)*F_141(x, k_0)*F_144(x))
Eq(F_141(x, k_0), F_142(x) + F_143(x, k_0))
Eq(F_142(x), F_1(x) + F_36(x))
Eq(F_143(x, k_0), F_68(x, k_0) + F_97(x, k_0))
Eq(F_144(x), F_145(x) + F_22(x))
Eq(F_145(x), F_1(x) + F_146(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_11(x)*F_144(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_11(x)*F_150(x))
Eq(F_150(x), F_151(x) + F_16(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_11(x)*F_142(x)*F_144(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 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